Question

Which of the following quantities is always negative in SHM?

• A. $\overrightarrow{F}.\overrightarrow{a}$
• B. $\overrightarrow{F}.\overrightarrow{r}$
• C. $\overrightarrow{v}.\overrightarrow{r}$
• D. $\overrightarrow{a}.\overrightarrow{r}$

Answer 1

Answer: (B), (D)

$\overrightarrow{F}.\overrightarrow{r}$
$\overrightarrow{a}.\overrightarrow{r}$

• Since force and acceleration is always in opposite direction of displacement. so the dot product of displacement $\overrightarrow{r}$ with $\overrightarrow{F}$ and $\overrightarrow{a}$ is always smaller than zero. $\Rightarrow$ B and D are correct
• Force and acceleration are always in same direction so dot product of $\overrightarrow{F}$ and $\overrightarrow{a}$ is always greater then zero. $\Rightarrow$ A is incorrect
• Velocity and displacement are not always in the same direction so dot product of
  $\overrightarrow{v}$ and $\overrightarrow{r}$ is sometimes greater then zero and sometimes less then zero $\Rightarrow$ C is incorrect